Question

Find \[10\% \] of a number.

Answer 1

Hint: Use the definition of percentage to find the values. Percent means out of \[100\], it is a number expressed as a fraction of \[100\].

Complete step by step solution:
To convert the number to the percentage we simply divide it by \[100\] if the total is \[100\]. But in case the total is not \[100\], we have to convert the denominator to \[100\] by using the method of proportion. For example, if the total is \[200\], we may divide both the numerator and the denominator by \[2\] so that the denominator becomes \[100\].
Example: If the total is \[100\], then a part equal to \[30\] will be \[30\% \] of the whole.
In simple terms an expression may be deduced that,
\[\dfrac{{part}}{{whole}} = \dfrac{{percentage}}{{100}}\]….(1)
In the question the “part” from the above equation needs to be found.
Percentage \[ = \] \[10\]
\[\therefore \] \[part = \dfrac{{10}}{{100}} \times whole\]
\[ \Rightarrow part = \dfrac{1}{{10}} \times whole\]
\[ \Rightarrow part = \dfrac{{whole}}{{10}}\].

Hence \[10\% \] of a number \[ = \] \[\dfrac{{number}}{{10}}\].

For example \[10\% \] of \[200\] \[ = \] \[\dfrac{{200}}{{10}}\] \[ = \] \[20\].

Note: It must be noted that the term “cent” means \[100\] percentage always means out of \[100\]. It is a special fractional form in which the denominator is always \[100\]. For this reason, the denominator in the right-hand side of the equation (1) is always \[100\].